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21,19,17,15,13,11..... how to put this sequence in an explicit form

1 Answer

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This sequence is arithmetic because we add -2 to each term to get the next term. So d = -2 is the common difference.

The starting term is a1 = 21

Therefore the nth term formula is

an = a1 + d(n-1)

an = 21 + (-2)(n-1)

an = 21 - 2n + 2

an = -2n + 23 which is the final answer

note how plugging in n = 1 leads to

an = -2n + 23

a1 = -2*1 + 23

a1 = -2 + 23

a1 = 21 which is the proper first term we want

So that helps partially confirm the answer. I'll let you check the other terms.

User Cppiscute
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